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RevMexAA (Serie de Conferencias), 46, 56–60 (2015)

GALACTIC DYNAMICAL STRUCTURE REVEALED BY VLBI

ASTROMETRY

N. Sakai1

RESUMEN

Astrometrıa es el metodo mas directo y preciso para revelar la estructura 3D de la Vıa Lactea. En este artıculorevisare la estructura Galactica basada en resultados del VLBI. En primer lugar se introducen algunos conceptosbasicos de astrometrıa con VLBI y areglos existentes de VLBI. Luego, se muestran algunos resultados cientıficosrecientes usando astrometrıa VLBI, en particular (i) Parametros fundamentales de la Vıa Lactea, (ii) La curvade rotacion de la Vıa Lactea, y (iii) El brazo (principal) de Perseus. Finalmente describo brevemente algunasposibilidades interesantes para astrometrıa de gas y estrellas en la era de Gaia.

ABSTRACT

Astrometry is the most direct and accurate method to reveal the 3D structure of the Milky Way. I reviewthe Galactic structure based on VLBI astrometry results. First, I introduce some basic concepts of VLBIastrometry and actual VLBI arrays. Then, I show some recent scientific results with VLBI astrometry, namely(i) Fundamental parameters of the Milky Way, (ii) The rotation curve of the Milky Way, and (iii) The Perseus(main) arm of the Milky Way. Finally, I briefly describe future prospects for gas and stellar astrometry in theGaia era.

Key Words: astrometry — Galaxy: structure — techniques: interferometric

1. GENERAL

1.1. Astrometry

Astrometry aims to measure positions, distances,and motions of astronomical objects directly and ac-curately. Thanks to the motion of the earth aroundthe sun, a target shows an apparent elliptical motionprojected onto the celestial sphere. The semi-majoraxis of this ellipse is called the trigonometric parallax(π), which is defined by:

π =1AU

d, (1)

where AU is the astronomical unit and d is the dis-tance to the target. Note that 1 parsec (pc) is definedas 1 AU divided by 1 arcsecond.

Trigonometric parallaxes are called the “goldstandards”, since geometric distances can be mea-sured using the parallax without any assumptions(see equation 1). Precise distance measurements areimportant in astronomy, since they are related tosize, luminosity, mass, and ages of most objects.Also, the parallactic distance is a standard of thecosmic ladder, and therefore astrometry contributesto many astronomical fields (e.g., de Grijs 2013).

1Mizusawa VLBI Observatory, National Astronomi-cal Observatory of Japan, Mitaka, Tokyo 181-8588(nobuyuki.sakai@nao.ac.jp).

Proper motion (µ), the apparent tangential mo-tion of a target projected onto the celestial sphere,is another observable quantity in astrometry, whichoriginates in the target motion (e.g., due to Galac-tic rotation). The units of proper motion are oftengiven in arcsecond yr−1 or milliarcsecond yr −1. Thetangential velocity, vt (in km s−1), can be obtainedfrom the proper motion and the distance through:

vt = κ · µ · d, (2)

where κ ∼ 4.74. Note that µ and d are expressedin arcsecond yr−1 and pc, or milliarcsecond yr−1

and kpc, respectively. A combination of the tangen-tial velocity and the line-of-sight velocity (measuredthrough the Doppler effect) tells us 3D motion of atarget.

In terms of history of astrometry, the Hipparcossatellite, the first space experiment devoted to pre-cision astrometry, was launched in 1989 (Perryman1989). It brought us stellar parallaxes with accura-cies (∆π) of ∼ 1 milliarcsecond (mas). The informa-tion was available for a volume of ∼ 100 pc aroundthe Sun, since ∆π

π< 0.1 is required to avoid the

Lutz-Kelker bias2 (Lutz & Kelker 1973).Nowadays, Very Long Baseline Interferometry

(VLBI) arrays at radio wavelengths are used to carry

2<

1

π> 6= 1

<π>

56

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VLBI ASTROMETRY 57

out Galactic scale astrometry, and to understand the3D structure and dynamics of the Milky Way. Weintroduce VLBI in the following section.

1.2. Very Long Baseline Interferometry (VLBI)

Advantage: The highest angular resolution

Until now VLBI at radio wavelengths has achievedthe highest angular resolution of any wavelength.The angular resolution can be estimated as ∼ λ

D

where λ is the observing wavelength and D is thelength of the baseline. If we set D = 8,600 km and λ

= 1.3 cm based on Very Long Baseline Array (VLBAin the USA), then an angular resolution of ∼ 0.3 mascan be achieved. If thermal (random) error is dom-inant in VLBI observations, the centroid accuracywith VLBI for a compact source can be roughly es-timated as λ

D· 1/2 · 1

SNR, where SNR is the signal-to-noise ratio. Again, if we set D = 8,600 km andλ = 1.3 cm with a typical SNR for VLBA observa-tions, then a centroid accuracy of ∼ 10 microarcsec-ond (µas) is obtained.

However, systematic errors are dominant inVLBI observation (e.g., due to tropospheric zenithdelay residuals). To reduce the systematic errors,relative VLBI observations are performed, in whichthe target and an adjacent reference (e.g., a distantQSO) source are observed alternately with an appro-priate switching cycle depending on the observingwavelength. The centroid (position) accuracy (∆s)with relative VLBI observations can be roughly es-timated as:

∆s =c∆τ

|D|· θsep, (3)

where c is the speed of light, ∆τ is the delay, anobservable quantity in VLBI observations, and θsep

is the separation angle between the target and thereference source. If we set D = 8,600 km, c∆τ =2 cm, and θsep = 1.0 deg in equation 3, then ∆s ∼10 µas is obtained.

As we can see, using relative VLBI astrometry wecan carry out Galactic scale astrometry, measuring3D positions and motions of Galactic objects.

Disadvantage: Low sensitivity Relative VLBIastrometry allows us to conduct Galactic scale as-trometry with a positional accuracy of ∼10 µas, assummarized in Reid & Honma (2014). However, inVLBI, the size of the observed source (θ0) should becomparable to, or smaller than, the angular resolu-tion of VLBI, λ

D, otherwise the source flux is reduced

significantly (for more details see Sasao & Fletcher

2005). This condition for VLBI is described as:

θ0 ≤λ

D. (4)

Using equation (4), we can write the intensity Iν andflux density Fν of the source as follows:

Iν =2kTB

λ2≤

2kTB

θ20D

2, and Fν =

2kTB

λ2

πθ20

4≤

πkTB

2D2,

(5)where k = 1.381 × 10−23 J K−1 is the Boltzmannconstant and TB is the brightness temperature of thesource. If we set the minimum detectable flux den-sity (Fνmin) by VLBI, we can write the lower limit(TBmin) to the brightness temperature for the de-tectable source using equation (5) as follows:

TBmin ≃2D2

πkFνmin. (6)

If we set D = 2,300 km and Fνmin = 0.16 Jy from theVERA Status Report3 in equation (6), then TBmin ≃4×108 K. This means that VLBI astrometry can ob-serve only compact and non-thermal sources such as;AGNs, masers and pulsars. However, we are unableto observe thermal sources such as; stars or molecu-lar clouds.

In this paper, we especially focus on maserastrometry to discuss Galactic structure, because alarge number of masers (∼ 1,000) are distributed inGalactic star-forming regions and around late-typestars (e.g., Valdettaro et al. 2001), and also becausethey are bright and compact enough for VLBIastrometry.

1.3. VLBI arrays in the world

We briefly introduce VLBI arrays in the world asshown in Table 1. Galactic scale astrometry has beenled by VLBA, VERA, and partly EVN in the North-ern hemisphere. In fact, VLBA and VERA havesucceeded to measure a parallactic distance largerthan 10 kpc and 5 kpc with 10% error, respectively.The measurements are comparable to the size of theGalactic disk of ∼ 20 kpc, and therefore we can studythe 3D structure and dynamics of the Milky Way us-ing these results.

The Long Baseline Array (LBA) is the only arrayin the Southern hemisphere. This array is crucial tostudy the Milky Way as a whole.

3http://veraserver.mtk.nao.ac.jp/restricted/

CFP2012/status12.pdf

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58 SAKAI

TABLE 1

VLBI ARRAYS IN THE WORLD

Array Antenna diameter Beam Maximum Baseline Image Memo

and size at baseline sensitivity∗ sensitivity†

number in array 22 GHz (km) (mJy) (µJy)

VLBA 25 m × 10 0.3 mas 8,600 5‡ 44‡

VERA 20 m × 4 1.2 mas 2,300 14§ 356§ Dedicated to astrometry

EVN 14 m − 100 m, 0.2 mas 2,900 − 1 − 43∗∗ Astrometry has been conducted

× ∼ 10 12,000 10∗∗ at a frequency ≤ 6.7 GHz

LBA 22 m − 70 m, 0.3 mas 1,700 − 1 − 50†† The only VLBI array in

× ∼ 7 9,800 24†† the Southern hemisphere

∗ An integration time of 120 seconds and an observing frequency of 22 GHz were assumed for the continuum source.† An integration time of 8 hours and an observing frequency of 22 GHz were assumed for the continuum source.‡ The values were estimated based on Choi et al. (2014) and

https://science.nrao.edu/facilities/vlba/docs/manuals/oss2013b/referencemanual-all-pages§ The values were estimated based on http://veraserver.mtk.nao.ac.jp/restricted/CFP2015A/status15A.pdf∗∗ The values were estimated based on Rygl et al. (2012), http://www.evlbi.org/user_guide/EVNstatus.txt

and http://www.atnf.csiro.au/vlbi/calculator_2009/†† The values were estimated based on http://www.atnf.csiro.au/vlbi/calculator_2009/

TABLE 2

A HISTORY OF DETERMINATIONS OF THE GALACTIC CONSTANTS

Paper # of sources R0 Θ0 Method

(kpc) (km s−1)

Reid et al. 2009 18 8.40 ± 0.60 254 ± 16 Least squares fit

Honma et al. 2012 52 8.05 ± 0.45 238 ± 14 MCMC

Reid et al. 2014 103 8.34 ± 0.16 240 ± 8 MCMC

2. RESULTS & DISCUSSIONS

2.1. Fundamental parameters of the Milky Way

Astrometry can be used to determine fundamen-tal parameters of the Milky Way such as the Galacticconstants (R0, Θ0). The accuracy of the Galacticconstants have increased with the increasing num-ber of astrometric results, as shown in Table 2. Reidet al. (2009) determined Galactic constants of (R0,Θ0) = (8.4 ± 0.6 kpc, 254 ± 16 km s−1) with 18astrometry results, which are different from the IAUrecommended values of (R0, Θ0) = (8.5 kpc, 220 kms−1) especially for Θ0. Note that the sum of Θ0 andV⊙ (peculiar solar motion in the direction of Galacticrotation) was well constrained in Reid et al. (2014),while Θ0 and V⊙ showed a negative correlation.

The difference between Θ0 = 254 and 220 km s−1

brings a big impact on Milky Way structure, sincethe mass of the dark matter halo scales as (Θ0)

∼3

(e.g., Navarro, Frenk & White 1997). It means that

the mass of the Milky Way is increased by ∼ 50 %compared to the previous result. This big impactwas explained in the NRAO press release 4. The im-plied greater mass of the Milky Way means that ithas a mass equal to that of the Andromeda galaxy.The Milky Way is not the little sister of the An-dromeda galaxy anymore, they look like twins.

2.2. The Rotation Curve of the Milky Way

Reid et al. (2014) compiled 103 VLBI astrome-try results, as shown in Figure 1. Using these results,Figure 2 shows a rotation curve of the Milky Way.The important point in Figure 2 is that the rotationcurve is flat between ∼ 5 and 15 kpc of Galactocen-tric radii (R). This is indicative of large amounts ofdark matter.

Also, Figure 2 gives us hints about the effects ofasymmetric potentials (e.g., due to the bar and spiral

4http://www.nrao.edu/pr/2009/mwrotate/

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VLBI ASTROMETRY 59

Fig. 1. Previous VLBI astrometry results mainly basedon Reid et al. (2014), which are superimposed on aschematic view of the Milky Way. The results displayclockwise galactic rotations. ⊙ denotes the solar posi-tion.

arms). The results with R less than 5 kpc may beaffected by the bar potential. Fluctuations are seenat ∼ 6 ≤ R ≤ ∼ 10 kpc, which indicates the effectof spiral arms. We will further discuss the effect ofspiral arms in the next section.

2.3. Systematic peculiar (non-circular) motions inthe Perseus arm

The Perseus arm traced by star and gas is one ofthe main arms in the Milky Way (e.g., Churchwellet al. 2009). The Perseus arm has been studiedby many authors (e.g., Roberts 1972; Georgelin &Georgelin 1976; Drimmel & Spergel 2001; Russeil2003).

Sakai et al. (2012) and (2013) studied the 3Dstructure and kinematics of the Perseus arm usingVLBI astrometry (see Figures 3 and 4). Figure 3shows the peculiar motions in the U -V plane, onwhich several arms are superimposed. Note that U

and V are directed to the Galactic center and Galac-tic rotation, respectively. The sources in the Perseusarm are located in the lower right of the figure, mean-ing that the sources are moving systematically to-ward the Galactic Center, and lag behind Galacticrotation.

Sakai et al. (2012) determined averaged peculiarmotions of (Umean, Vmean) = (11 ± 3, −17 ± 3) kms−1 with seven sources in the Perseus arm with ∼ 4-σsignificance. Figure 4 represents a schematic view of

Fig. 2. Rotation curve of the Milky Way based on theastrometry results shown in Figure 1.

the systematic peculiar motions. These systematicpeculiar motions were also confirmed by Choi et al.(2014), who determined averaged peculiar motionsof (Umean, Vmean) = (9.2 ± 1.2, −8.0 ± 1.3) km s−1

with 25 sources in the Perseus arm. The system-atic peculiar motion is consistent with the Galac-tic shock model proposed by Fujimoto (1968) andRoberts (1969).

3. FUTURE PROSPECTS IN THE GAIA ERA

Gaia, the next generation satellite devoted to as-trometry, was lunched on December 19, 2013. Gaiawill conduct astrometry for one billion stars with atarget accuracy of 10 µas, which will enable us tomeasure distances out to 10 kpc with 10 % error.Gaia and VLBI have a mutually complementary re-lationship in terms of both quantity and quality ofGalactic astrometry.

For instance, Gaia will bring us a large sampleof stellar astrometry, while at optical wavelengths itwill suffer from dust extinction in the Galactic disk.On the other hand, VLBI astrometry at radio wave-lengths can observe the entire Galactic disk and, assuch, it will provide us with astrometric results to-ward several hundreds star-forming regions (SFRs).

A combination of star and gas astrometry willbe a powerful tool to discriminate among differentGalactic dynamical models, such as the density-wavetheory (Lin & Shu 1964) and the “recurrent andtransient spiral” proposed by N-body simulations(e.g., Baba et al. 2013), since various models havepredicted different results for the distribution and

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60 SAKAI

Fig. 3. U vs. V plane on which previous VLBI astrometryresults are superimposed (from Sakai et al. 2012). U andV are peculiar (non-circular) motions, and are directed tothe Galactic Center and Galactic rotation, respectively.For deriving the peculiar motions, we assumed Galacticconstants of (R0, Θ0) = (8.33 kpc, 240 km s−1), peculiarsolar motions of (U⊙, V⊙, W⊙) = (11.1 ± 1, 12.24 ± 2,7.25 ± 0.5) km s−1, and a flat Galactic rotation (i.e., Θ(R)= Θ0). Different colored circles mean different arms (Red= Perseus arm; Blue = Outer arm; Black = Local arm).

Fig. 4. Schematic view of the systematic peculiar motionsseen in the Perseus arm (from Sakai et al. 2013).

motions of gas and stars. In the next decade, as-trometry will allow us to understand the origin andevolution of the spiral arms as well as that of theMilky Way.

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